#include <string>
#include <vector>
using namespace std;
/*
 * @lc app=leetcode.cn id=72 lang=cpp
 *
 * [72] 编辑距离
 */

// @lc code=start
// dp[i][j] s1的前i个和s2的前j个操作数
// d[i][j] = 
// 1.  s[i] = w[j], dp[i - 1][j - 1]
// 2.  s[i] != w[j], min(dp[i - 1][j], dp[i - 1][j - 1], dp[i][j - 1]) + 1
class Solution {
public:
    int minDistance(string word1, string word2) {
        int sz1 = word1.size(), sz2 = word2.size();
        vector<vector<int>> dp(sz1 + 1, vector<int>(sz2 + 1));
        for (int i = 1; i <= sz1; i++) dp[i][0] = i;
        for (int j = 1; j <= sz2; j++) dp[0][j] = j;
        for (int i = 1; i <= sz1; i++) {
            for (int j = 1; j <= sz2; j++) {
                if (word1[i - 1] == word2[j - 1]) {
                    dp[i][j] = dp[i - 1][j - 1];
                }
                else {
                    dp[i][j] = min(dp[i - 1][j - 1], min(dp[i - 1][j], dp[i][j - 1])) + 1;
                }
            }
        }
        return dp[sz1][sz2];
    }
};
// @lc code=end

